A former head of Iran's Revolutionary Guards on Sunday threatened his country would turn the Israeli cities of Haifa and Tel Aviv "to dust" if the US attacks targets in Iran.

"If America takes any measures after our military response, we will turn Tel Aviv and Haifa to dust," Mohsen Rezai, who currently heads the Expediency Council, a top state body, said in a Tweet, according to AFP.

His warning came after President Donald Trump warned on Saturday that the US would target 52 sites "important to Iran & Iranian culture" and hit them "very fast and very hard" if the Islamic Republic attacked American personnel or assets.

"Mr. Trump, you tweeted that you will attack 52 targets in Iran?" Rezai fired back on Sunday.

"You have said that you will attack again if Iran gets revenge? Be sure that Iran will turn Haifa and Israel's centers to dust in a way that Israel would be erased from the face of the earth," he warned.

Trump's tweet also drew condemnation from Iranian Foreign Minister Mohammad Javad Zarif who responded on Twitter saying "targeting cultural sites is a WAR CRIME".

The back-and-forth threats between the US and Iran follow the elimination of Qassem Soleimani, commander of the Islamic Revolutionary Guards Corps' Quds Force, in a US drone strike Friday near Baghdad airport.

The attack was ordered by Trump, who said the Quds commander had been planning an "imminent" attack on US diplomats and forces in Iraq.

Soleimani’s successor, Brig. Gen. Esmail Ghaani, threatened the US hours after the air strike, saying, “Everyone should be patient a little to see the bodies of American soldiers all over the Middle East.”

Iran's Supreme Leader Ayatollah Ali Khamenei vowed "severe revenge" for the death of Soleimani.